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  • Locus of the midpoint of any focal chord of is<div class='qna-opt

Locus of the midpoint of any focal chord of \mathrm{y^{2}=4 a x} is

Option: 1

\mathrm{y^{2}=a(x-2 a)}


Option: 2

\mathrm{y}^{2}=2 \mathrm{a}(\mathrm{x}-2 \mathrm{a})


Option: 3

\mathrm{y^{2}=2 a(x-a)}


Option: 4

 None of these


Answers (1)

best_answer

Let the midpoint be \mathrm{P(h, k)}

Equation of this chord is
\begin{gathered} T=S_{1} . \\ \text { i.e., } y k-2 a(x+h)=k^{2}-4 a h \\ \text { It must pass through }(a, 0) \\ \Rightarrow \quad 2 a(a+h)=k^{2}-4 a h \end{gathered}
Thus required locus is

\mathrm{y}^{2}=2 \mathrm{ax}-2 \mathrm{a}^{2}

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